It is important to understand and hence have the means to control the intrinsic morphologies of materials grown by the LPE process. This is particularly so if the method is utilized to make devices, which, for efficient operation rely upon planar interfaces between the layers of a multilayer structure. The double heterostructure laser is such a device and the materials with which this paper is concerned are commonly used in the fabrication of this device. The particular morphology with which this paper is concerned is that of waves on the surfaces of grown layers. A brief discussion will be presented of the distinction between waves and terraces, or microfacets. An LPE system will be described in which the growth rate is essentially time independent. In this apparatus layers of both GaAs and Ga0.65Al0.35As have been grown both on nominal (100) substrates and on substrates 1° off that orientation at a range of growth rates. The wavelength of the surface waves has been found to be proportional to the reciprocal of the square root of the growth rate. The observed wavelengths vary in the range between 40 μm at a growth rate of 0.7x10-7 cm s-1 and 6 μm at 1.8x10-6 cm s-1. On (100) substrates it is observed that terraces and waves may coexist. The terrace edges are lines of intersection of the mean plane of the surface with the singular surface. The waves are found to be parallel to the terraces. This may be either due to the terraces presenting a regular series of initial perturbations to the equilibrium form of the surface or due to the strong anisotropy in the surface tension near a singularity. First order morphological stability theory has been applied to the situation. This confirms the observed dependence of wavelength on growth rate and gives a reasonable agreement with the constant of proportionality which has been observed. © 1977.